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Research Papers

# Parametric Design and Power-Flow Analysis of Parallel Force∕Velocity Actuators

[+] Author and Article Information
Dinesh Rabindran

Department of Mechanical Engineering, The University of Texas at Austin, Austin, TX 78703dineshr@mail.utexas.edu

Delbert Tesar

Department of Mechanical Engineering, The University of Texas at Austin, Austin, TX 78703tesar@mail.utexas.edu

This concept is protected by a United States provisional patent.

$g$ refers to the $g$-function or the kinematic influence coefficient (24) (in this case, it is the constant gear train velocity ratio).

The velocity-related losses can be incorporated into this term by considering an additional ventilation∕splash loss factor as suggested by Müller (15) (p. 19).

Scale-invariant mesh loss-factors were assumed in Ref. 20.

The rolling power (15) refers to the power through a planetary gear and a sun (or ring) gear, measured by an observer fixed to the carrier driving this (planetary) gear. The virtual power (20) is defined as the power through an arbitrary gear measured by an observer attached to any planetary carrier in this train. Therefore, rolling power is a special case of virtual power (when the observer is attached to the carrier connected to the planetary gear of interest).

We base our argument about futile power on Müller’s work (15) who originally presented it. However, the futile power term might be fictitious because it is measured by an observer attached to the planet carrier (FA shaft in our case). We invite comments regarding this issue from the community for greater clarity on the physical meaning of this term.

In a differential mechanism such as the PFVA, the output velocity is a weighted sum of the input velocities and the torques on all component shafts bear a constant ratio. See Fig. 1 in Ref. 24 for some multidomain examples of differential mechanisms.

J. Mechanisms Robotics 1(1), 011007 (Aug 05, 2008) (10 pages) doi:10.1115/1.2959100 History: Received January 03, 2008; Revised June 20, 2008; Published August 05, 2008

## Abstract

In this paper we introduce a dual-input actuator, based on an epicyclic gear train, called parallel force∕velocity actuator (PFVA) designed for variable response manipulation. The focus of this work is to formulate a parametric representation for internal and external power flows, and effective inertia in this actuator. Dimensionless criteria have been developed to judge the design of a PFVA, based on the above phenomena. These criteria are then related to two fundamental dimensionless parameters of a PFVA: (i) a design parameter called the relative scale factor that describes the relative kinematic scaling between the two inputs of the PFVA and (b) an operational parameter called the velocity mixing ratio that represents the velocities of the inputs relative to each other. Some numerical examples have been considered using PFVA designs based on positive-ratio drives to convey the practical implication of our parametric models. Based on this study a set of design and operational guidelines has been suggested, which we believe will be useful to the designer in evaluating PFVA designs and operational scenarios on the basis of power-flow and effective inertias. As a representative result, it was observed that the efficiency of a PFVA decreases approximately 19% from the basic efficiency when the relative scale factor was increased approximately 6.5 times (from 4.7 to 25.27) and the velocity mixing ratio was increased 10 times (from 4.16 to 41.6).

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## Figures

Figure 1

A continuum of geared electromechanical actuators (EMAs) (10). The dynamic response of the actuator varies along the spectrum depending on the gear reduction used. Also shown is an example of a DISO epicyclic gear train that can be used in a PFVA.

Figure 2

Variation of SISO efficiencies with respect to the relative scale factor ρ̃ for the commercially available SA-series differentials from Andantex Inc., Wanamassa, NJ (22,18). ηv→o is the basic efficiency of the drive train.

Figure 3

Mechanical efficiency analysis of a DISO PFVA as the superposition of a SISO FA and VA

Figure 4

Variation of PFVA’s overall mechanical efficiency η as a function of various designs (based on different values for ρ̃) and various operating conditions (based on different values for λ̃)

Figure 5

Representation of exchange of total power, rolling power, and coupling power between the VA and the output of the PFVA for Example 2

Figure 6

Graph showing internal and external power flows in a positive-ratio PFVA: (a) No futile power flow and (b) futile power-flow condition

Figure 7

Futile power ratio for varying values of the relative scale factor ρ̃ and the inverse of velocity mixing ratio λ̃

Figure 8

Variation of effective inertia ratio Ĩeff as a function of VMR for various example PFVA designs (see Appendix ). Design Example 2 corresponds to the PFVA testbed being set up at the University of Texas Robotics Research Group Lab in Austin, TX.

Figure 9

Planar four-bar linkage driven by a PFVA

Figure 10

Equivalent link representation of the four bar mechanism in Fig. 9

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